Chapter_2

# Chapter_2 - a a t t a v t v x − → Area of rectangle Ch...

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Ch 2: Kinematics in One Dimension Focus: Position (x), Velocity (v), Acceleration (a) x(t) as area under v(t), v(t) as area under a(t) Catch- up, crash! O Reference frame Origin Scale Meters x t Clock Seconds Characterizing Motion Position varies with time Newton (1642-1727) Witchcraft! Apple attracted to Earth: Attraction might extend to the moon!

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Ch 2: Kinematics in One Dimension O x t 1 Velocity (m/sec) 2 2 1 2 1 2 t t x x t x x v = = Average Velocity: (slope of chord) x t Instantaneous Velocity: (slope of curve) 0 as = t dt dx v x Newton: “Fluxions”
Ch 2: Kinematics in One Dimension O v x t 1 Instantaneous Acceleration: (slope of curve) 0 as = t dt dv a x x Acceleration (m/sec 2 ) 2 2 1 2 1 2 t t v v t v x a x x x = = Average Acceleration: (slope of chord) v x t

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Ch 2: Kinematics in One Dimension = + = t t t n x n x x n t a t t v t v 0 ) ( ) ( ) ( 0 Velocity as Area under Acceleration vs Time Curve a x (t) t t 0 t 2 t 1 t n-1 t n t ) ( t a t v x x = Integral = Area under curve + t t x x t a dt v t v 0 ) ' ( ' ) ( 0 Newton: “Fluents”
Ch 2: Kinematics in One Dimension Velocity as Area under Acceleration vs Time Curve a x (t) t t 0 t Example: Constant acceleration

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Unformatted text preview: a a ) ( ) ( t t a v t v x − + → Area of rectangle Ch 2: Kinematics in One Dimension ∑ = ∆ + = t t t n x n n t v t t x t x ) ( ) ( ) ( Position as Area under Velocity vs Time Curve v x (t) t t t 2 t 1 t n-1 t n Integral = Area under curve ∫ + → t t x t v dt x t x ) ' ( ' ) ( ∆ t ) ( t v t x x ∆ = ∆ Ch 2: Kinematics in One Dimension Position as Area under Velocity vs Time Curve ) ( t t a v v − + = t t v t v a (t-t ) Triangle Rectangle Example: Constant a 2 2 1 ) ( ) ( ) ( t t a t t v x t x − + − + = Rectangle + Triangle Ch 2: Kinematics in One Dimension a v v t t − = − ⇒ ) ( 2 2 2 x x a v v − + = For constant acceleration a , initial position x , initial velocity v : 2 2 1 ) ( ) ( t t a t t v x x − + − + = ) ( t t a v v − + = Memorize this! Memorize this!...
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Chapter_2 - a a t t a v t v x − → Area of rectangle Ch...

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